You are in charge of funding medical research for an imaginary country.
There are 11 diseases in this country. Of disease sufferers, 80%
suffer from disease A, 11% from disease B, and 1% each suffer from each of
the remainin 8 diseases C-K. Every $1 billion you spend on researching a
disease reduces the absolute number of sufferers from that disease by 1%.
(To clarify: that means that if you spend $2 billion on disease B, you
reduce the total number of disease suffers by 2% of 11%.) You have $11
billion. What is your optimal spending pattern?
(You can make this problem more interesting by introducing diminishing
returns. Suppose the first $1 billion spent on a disease reduces deaths
from that disease by 1%, the next $1 billion by 1/2%, the next $1 billion
by 1/4%, etc.)
Does spending more on diseases A and B make sufferers of other diseases
"second class citizens"? Discuss.
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